# What is the logarithm of zero?

Oct 15, 2014

The logarithm of 0 is undefined.

Note that the logarithm base $b$ of a number $n$ answers the problem

${b}^{x} = n$

Substituting $n$ with $0$
${b}^{x} = 0$

However, no matter what $b$ or $x$ is, ${b}^{x}$ will never be 0.